### Evaluate the Integral #### Problem Statement: Evaluate the integral: \[ \int \frac{5x + 8}{x^3 + x} \, dx \] #### Answer Choices: a. \( 8\ln x + 5\tan^{-1} x + C \) b. \( \frac{-4}{x^2} - \frac{5}{x} + C \) c. \( 4\ln x + 5\tan^{-1} x - 8\ln(x^2 + 1) + C \) d. \( 8\ln x + 5\tan^{-1} x - 4\ln(x^2 + 1) + C \) e. \( 8\ln x - \tan^{-1} x - 4\ln(x^2 + 1) + C \) In this problem, you are required to evaluate the integral given and choose the correct answer from the provided options. The correct answer is marked with a purple circle.